Codebook With Nested Structure

ABSTRACT

A multi-rank beamforming (MRBF) scheme in which the downlink channel is estimated and an optimal precoding matrix to be used by the MRBF transmitter is determined accordingly. The optimal precoding matrix is selected from a codebook of matrices having a recursive structure which allows for efficient computation of the optimal precoding matrix and corresponding Signal to Interference and Noise Ratio (SINR). The codebook also enjoys a small storage footprint. Due to the computational efficiency and modest memory requirements, the optimal precoding determination can be made at user equipment (UE) and communicated to a transmitting base station over a limited uplink channel for implementation over the downlink channel.

This application is a Division of U.S. patent application Ser. No.12/026,120, filed Feb. 5, 2008, which in turn claims the benefit under35 U.S.C. 119(e) of U.S. Provisional patent application Ser. No.11/554,278, filed Oct. 30, 2006, and U.S. patent application Ser. No.11/674,330, filed Feb. 13, 2007, the entire contents and file wrappersof which are hereby incorporated by reference for all purposes into thisapplication.

FIELD OF THE INVENTION

The present invention relates to the field of wireless communications,particularly wireless, high-rate communications using multiple-antennasystems.

BACKGROUND INFORMATION

The hostility of the wireless fading environment and channel variationmakes the design of high rate communication systems very challenging. Tothis end, multiple-antenna systems have been shown to be effective infading environments by providing significant performance improvementsand achievable data rates in comparison to single antenna systems.Wireless communication systems employing multiple antennas both at thetransmitter and the receiver demonstrate tremendous potential to meetthe spectral efficiency requirements for next generation wirelessapplications.

Moreover, multiple transmit and receive antennas have become an integralpart of the standards of many wireless systems such as cellular systemsand wireless LANs. In particular, the recent development of UMTSTerrestrial Radio Access Network (UTRAN) and Evolved-UTRA has raised theneed for multiple antenna systems to reach higher user data rates andbetter quality of service, thereby resulting in an improved overallthroughput and better coverage. A number of proposals have discussed andconcluded the need for multiple antenna systems to achieve the targetspectral efficiency, throughput, and reliability of EUTRA. While theseproposals have considered different modes of operation applicable todifferent scenarios, a basic common factor among them, however, is afeedback strategy to control the transmission rate and possibly avariation in transmission strategy.

The performance gain achieved by multiple antenna system increases whenthe knowledge of the channel state information (CSI) at each end, eitherthe receiver or transmitter, is increased. Although perfect CSI isdesirable, practical systems are usually built only on estimating theCSI at the receiver, and possibly feeding back some representation ofthe CSI to the transmitter through a feedback link, usually of limitedcapacity. The transmitter uses the information fed back to adapt thetransmission to the estimated channel conditions.

Various beamforming schemes have been proposed for the case of multipletransmit antennas and a single receive antenna, as well as for higherrank MIMO systems, referred to as multi-rank beamforming (MRBF) systems.In MRBF systems, independent streams are transmitted along differenteigenmodes of the channel resulting in high transmission rates withoutthe need for space-time coding.

In addition to performance considerations, it is also desirable toachieve the highest possible spectral efficiencies in MIMO systems withreasonable receiver and transmitter complexity. Though space-time codingis theoretically capable of delivering very high spectral efficiencies,e.g. hundreds of megabits per second, its implementation becomesincreasingly prohibitive as the bandwidth of the system increases.

A need therefore exists for an MRBF scheme that is capable of highthroughput yet which can be implemented with reasonable complexity.

SUMMARY OF THE INVENTION

The present invention is directed to quantized, multi-rank beamforming(MRBF) methods and apparatus, and in particular, methods and apparatusfor precoding a signal transmitted in an MRBF system using an optimalprecoder selected in accordance with a channel quality metric. In anexemplary embodiment, the precoded signal is transmitted in a high-speeddownlink from a base station to user equipment (UE) and the channelquality metric includes a channel quality indicator (CQJ) that istransmitted to the base station from the UE.

In an exemplary embodiment of the present invention, optimal precoderselection can be carried out with low computational cost and complexityusing a precoding codebook having a nested structure which facilitatesprecoder selection. Moreover, the exemplary codebook requires lessmemory to store and yields better system throughput than those of otherschemes.

In a further exemplary embodiment, Signal to Interference and NoiseRatio (SINR) information for one or more active downlink streams is usedas a channel quality metric in selecting the optimal precoder.

The aforementioned and other features and aspects of the presentinvention are described in greater detail below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic block diagram of a wireless multiple-antenna MIMOcommunications system with quantized feedback of channel stateinformation.

FIG. 2 is a block diagram of an exemplary embodiment of a transmitter inaccordance with the present invention.

FIG. 3 is a block diagram of an exemplary embodiment of a receiver inaccordance with the present invention.

FIG. 4 is a flowchart of an exemplary embodiment of a method ofselecting a precoder matrix in accordance with the present invention.

FIG. 5 is a block diagram of an exemplary embodiment of a multi-codewordtransmitter in accordance with the present invention.

FIG. 6 is a block diagram of an exemplary embodiment of a multi-codewordlinear receiver in accordance with the present invention.

FIG. 7 is a block diagram of an exemplary embodiment of a multi-codewordsuccessive interference canceling receiver in accordance with thepresent invention.

DETAILED DESCRIPTION

An exemplary multiple-antenna communication system 100 with quantizedfeedback is schematically shown in FIG. 1. A transmitter 110, such as ata base station (“NodeB”), transmits from m transmitting antennas111.1-111.m over a fading channel 130 to n receiving antennas121.1-121.n coupled to a receiver 120, such as at user equipment (UE).The system 100 may be, for example, an orthogonal frequency-divisionmultiplexing (OFDM) system, in which each of a plurality of orthogonalsub-carriers is modulated with a conventional modulation scheme, such asquadrature amplitude modulation (QAM), quadrature phase shift keying(QPSK), or the like.

The system 100 also incorporates an exemplary multi-rank beamforming(MRBF) scheme with precoding in accordance with the present invention.The transmitter 110 controls the transmitting antenna outputs inaccordance with a set of precoding parameters, or a precoding matrix,which is selected based on an estimate of the channel 130 made at thereceiver 120.

At receiver 120, a channel estimator 125 provides an estimate of thechannel 130 to the receiver 120. One or more parameters determined as afunction of the channel estimate are also provided from the receiver 120to the transmitter 110 via a feedback channel. In an exemplaryembodiment, such fed-back parameters may include a channel qualityindicator (CQI) and the index of a recommended precoding matrix that thetransmitter 110 should use based on the channel conditions. Thedetermination of this information and its use by the transmitter aredescribed in greater detail below.

For purposes of analysis, a flat fading channel model is assumed inwhich the channel remains constant for each block of transmission. For amultiple-antenna system with m transmit and n receive antennas thecomplex baseband channel model can be expressed as follows:

y=Hx+z,  (1)

where x is the m×1 vector of the transmitted signals, y is the n×1vector of the received signals, H is an n×m matrix representing thechannel, and z˜

(0, N₀I) is the noise vector at the receiver.

FIG. 2 shows a block diagram of a transmitter 200 which incorporates anexemplary precoding scheme in accordance with the present invention. Adata stream d is first encoded by a forward error correction (FEC) block210 and then modulated by a modulator 220 to generate modulated symbolsu. The symbols u are provided to a serial-to-parallel converter (S/P)240 which generates k streams of symbols that are to be simultaneouslytransmitted during the current symbol transmission interval. k is alsoreferred to herein as the beam-forming rank. At output stage 240, thesymbol streams u₁, u₂, . . . u_(k), are subjected to pre-coding inaccordance with an m×k precoder matrix Q, as follows:

$\begin{matrix}{x = {{Qu} = \begin{bmatrix}u_{1} \\u_{2} \\\vdots \\u_{k}\end{bmatrix}}} & (2)\end{matrix}$

The precoder matrix Q is chosen from a finite set of possible precodermatrices, Q, referred to as the precoding codebook. An exemplaryprecoding codebook with a successive, or nested, structure is describedin greater detail below.

In the exemplary embodiment shown, the optimal precoder matrix isdetermined at the UE and an index representative thereof is fed-back tothe nodeB transmitter 200. A look-up block 250 uses the index to look-upthe corresponding precoder matrix Q and provides Q to the output stage240 which carries out the operation expressed by Eq. 2 to drive thecorresponding m antennas accordingly.

In addition to the precoder matrix index, the UE also feeds back the CQImetric to the nobeB transmitter 200. The CQI is used by a modulation andcoding scheme (MCS) block 260 to determine an appropriate MCScorresponding to the value of the CQI that is fed back. The MCSinformation includes a coding rate for the FEC encoder 210 and amodulation scheme selection for the modulator. Exemplary coding ratesmay include, for example, 1:3, 1:2, 3:4, 1:1, etc., and exemplarymodulation schemes may include QPSK, 16-QAM, 64-QAM, etc.

FIG. 3 shows a block diagram of an exemplary embodiment of a receiver300 for operation with the transmitter 200 of FIG. 2. The signals yreceived at the antennas of the receiver are provided to a detector 310and a channel estimator 320. In a preferred embodiment, the detector 310comprises a Linear Minimum Mean Squared Error (LMMSE) detector, althoughother detectors may be used. The detector 310 generates a stream of softoutputs or log likelihood ratios which are provided to a FEC decoder 330which recovers the data stream d′. The channel estimator 320 provides anestimate of the channel to the detector 310 and to a precoder matrix andCQI block 340. As described in greater detail below, the block 340 usesthe channel estimate to determine the optimal precoder matrix to be usedgiven the current channel conditions as well as a corresponding valuefor the CQI metric. The index of the precoder matrix thus determined andthe CQI are fed-back to the transmitter, which uses that information asdescribed above. The block 340 also provides the precoder matrix and themodulation scheme selection to the detector 310 and determines a codingrate to be used by the FEC decoder 330. The modulation and the codingrate correspond to the CQI, which is fed-back to the transmitter. Thetransmitter uses the CQI to determine the same coding rate for the FECencoder 210 and modulation scheme for the modulator 220 (see FIG. 2).

As mentioned above, an exemplary embodiment of an MRBF communicationssystem in accordance with the present invention uses a precodingcodebook with a successive, or nested, structure, which will now bedescribed. Exemplary methods and apparatus for optimal CQI-metric-basedprecoder selection are also described below, as well as thecorresponding Signal to Interference and Noise Ratio (SINR) computationsand LMMSE filters that take advantage of the proposed precodingstructure to reduce computational complexity.

Codebook

In an exemplary embodiment, a precoding codebook for use with atransmitter having M antennas comprises the following sets of unit normvectors:

{v _(i) ¹ εC ^(M) }, {v _(i) ² εC ^(M-1) }, . . . , {v _(i) ^(M-1) εC²},  (3)

where C^(N) is the N-dimensional complex space and the first element ofeach vector is real. The corresponding M×M precoding matrices are formedusing these vectors along with the unitary Householder matrix,

${{{HH}(w)} = {I - {2\frac{{ww}^{*}}{{w}^{2}}}}},$

which is completely determined by the non-zero complex vector w.Further, let HH(0)=I. More specifically, the corresponding precodingmatrices can be generated in accordance with the following expression:

$\begin{matrix}{{{A\left( {v_{i_{1}}^{1},v_{i_{2}}^{2},v_{i_{3}}^{3},\ldots}\mspace{14mu} \right)} = \begin{bmatrix}{v_{i_{1}}^{1},{{{HH}\left( {v_{i_{1}}^{1} - e_{1}^{M}} \right)}\begin{bmatrix}0 \\v_{i_{2}}^{2}\end{bmatrix}},} \\{{{HH}\left( {v_{i_{1}}^{1} - e_{1}^{M}} \right)}\;} \\{\begin{bmatrix}0 \\{{{HH}\left( {v_{i_{2}}^{2} - e_{1}^{M - 1}} \right)}\begin{bmatrix}0 \\v_{i_{3}}^{3}\end{bmatrix}}\end{bmatrix},\ldots}\end{bmatrix}},} & (4)\end{matrix}$

where e₁ ^(N)=[1, 0, . . . , 0]^(T)εC^(N). Letting N₁ denote the size ofthe vector codebook {v_(i) ¹εC^(M)}, N₂ denote the size of the vectorcodebook {v_(i) ²εC^(M-1)} and so on, the total number of M×M precodingmatrices that can be generated is N₁×N₂ . . . ×N_(M-1). The rank-Mprecoding codebook can be any subset, i.e., can include some or all ofthe M×M matrices out of these N₁×N₂ . . . ×N_(M-1) possible M×Mmatrices.

A precoding matrix for rank-k can be formed by selecting any k columnsof the possible M columns of the precoding matrix generated inaccordance with Eq. 4. An exemplary rank-3 precoder matrix correspondingto the first three columns can be constructed from three vectors v_(i)¹εC^(M), v_(j) ²εC^(M-1), v_(k) ³εC^(M-2) as follows:

$\begin{matrix}{{A\left( {v_{i}^{1},v_{j}^{2},v_{k}^{3}} \right)} = {\begin{bmatrix}{v_{i}^{1},{{{HH}\left( {v_{i}^{1} - e_{1}^{M}} \right)}\begin{bmatrix}0 \\v_{j}^{2}\end{bmatrix}},} \\{{{HH}\left( {v_{i}^{1} - e_{1}^{M}} \right)}\begin{bmatrix}0 \\{{{HH}\left( {v_{j}^{2} - e_{1}^{M - 1}} \right)}\begin{bmatrix}0 \\v_{k}^{3}\end{bmatrix}}\end{bmatrix}}\end{bmatrix}.}} & (5)\end{matrix}$

The rank-k precoding codebook is a set of such M×k precoding matricesand the maximum possible size of the codebook is N₁×N₂ . . . ×N_(M-1).Note that a rank-k precoding codebook of smaller size can be obtained byselecting only a few of the M×M matrices and then picking any k columnsout of each M_×_M matrix (the choice of the k column indices can alsovary from one matrix to the other).

In an exemplary embodiment, only the set of vectors {v_(i) ¹εC^(M)},{v_(i) ²εC^(M-1)}, . . . , {v_(i) ^(M-1)εC²} along with a set of complexscalars (described below) need be stored at the UE, thereby considerablylowering memory requirements at the UE, as compared to a schemeemploying unstructured matrix codebooks. At the base station, wherememory requirements are typically not as stringent, the matrixrepresentation of the codebook can be stored. Moreover, it is notnecessary for the UE to construct the matrix codewords to determine theoptimal precoder matrix and the corresponding LMMSE filter for a givenchannel realization.

Precoder Selection

FIG. 4 is a flow chart providing an overview of an exemplary method ofselecting the optimal precoder matrix in accordance with the presentinvention. Further details are set forth below. In an exemplaryembodiment, the method shown is carried out at the UE, such as shown inFIG. 3.

As shown in FIG. 4, an estimate of the channel is made at 410, asdescribed in greater detail below. At 420, based on the channel estimateH, an effective SINR is computed for each possible precoder matrix, ineach beamforming rank. At 430, the computed effective SINRs are comparedand for each rank, the precoder matrix with the greatest correspondingeffective SINR is selected. At 440, the transmission rates that areanticipated by using the precoder matrices selected at 430 aredetermined. At 450, the anticipated transmission rates are compared, andthe corresponding precoder matrix (and thus its rank) is selected forimplementation. At 460, the selected precoder matrix, or arepresentation thereof, such as an index, is provided to the transmitterand to the receiver for implementation. The selected precoding rank isimplicitly identified with the selected precoder matrix.

As mentioned above, in an exemplary embodiment, the precoder matrixselection takes place at the receiver (e.g., UE) and a representation(e.g., index) of the matrix selected is communicated to the transmitter(e.g., NodeB) via a feed-back channel. It is also contemplated by thepresent invention, however, that this process may be carried out at thetransmitter instead.

The various aspects of the method of FIG. 4 will now be described ingreater detail.

SINR Computations

In computing SINR, the channel model estimate can be expressed as H=[h₁,h₂, h₃, . . . h_(m)], where m is the number of transmit antennas. For aprecoded symbol stream p, where p=1, 2, . . . , k, one can define:

H _((p)) =[h _(p) , h _(p+1) , . . . h _(m)].  (6)

For a precoding matrix of rank k, denoted by A(v_(i) ¹, v_(i) ₂ ², . . ., v_(i) _(k) ^(k)), a matrix W_(i) ₁ _(, . . . , i) _(k) ^(1,k) can bedefined as follows:

W _(i) ₁ _(, . . . , i) _(k) ^(1,k) =[S _(i) ₁ _(, . . . , i) _(k)^(1,k) ]*S _(i) ₁ _(, . . . , i) _(k) ^(1,k),  (7)

where S_(i) ₁ _(, . . . , i) _(k) ^(1,k)=HA(v_(i) ₁ ¹, v_(i) ₂ ², . . ., v_(i) _(k) ^(k)) can be expanded as follows:

$\begin{matrix}{S_{i_{1},\mspace{11mu} \ldots \mspace{14mu},i_{k}}^{1,k} = {\begin{bmatrix}{{Hv}_{i_{1}}^{1},{{H_{(2)}v_{i_{2}}^{2}} - {2\frac{\alpha_{i_{1},i_{2}}^{1,2}}{\alpha_{i_{1}}^{(1)}}\left( {{Hv}_{i_{1}}^{1} - h_{1}} \right)}},...\mspace{14mu},} \\{{H_{(k)}v_{i_{k}}^{k}} - {2{\sum\limits_{j = 1}^{k - 1}{\frac{\alpha_{i_{j},\mspace{11mu} {\ldots \mspace{14mu} i_{k}}}^{j,k}}{\alpha_{i_{j}}^{(j)}}\left( {{H_{(j)}v_{i_{j}}^{j}} - h_{j}} \right)}}}}\end{bmatrix}.}} & (8)\end{matrix}$

The SINR for the precoded stream p obtained with an LMMSE detector isgiven by:

$\begin{matrix}{{{SINR}_{p} = {\frac{\rho}{\left( {\frac{I}{\rho} + W_{i_{1},\mspace{11mu} \ldots \mspace{14mu},i_{k}}^{1,k}} \right)_{p,p}^{- 1}} - 1}},} & (9)\end{matrix}$

where ρ=P/N₀, P is the average power per stream and N₀ is the noisevariance. The effective SINR for the rank-k precoding matrix A(v_(i) ₁¹, v_(i) ₂ ², . . . , v_(i) _(k) ^(k)) can be computed either as

${\exp\left( {\sum\limits_{p = 1}^{k}{\ln \left( {1 + {SINR}_{p}} \right)}} \right)} - {1\mspace{14mu} {or}\mspace{14mu} {as}\mspace{14mu} {\sum\limits_{p = 1}^{k}{{\ln \left( {1 + {SINR}_{p}} \right)}.}}}$

The LMMSE filter is given by:

$\begin{matrix}{{\left( {\frac{I}{p} + W_{i_{1},\mspace{11mu} \ldots \mspace{14mu},i_{k}}^{1,k}} \right)^{- 1}\left\lbrack S_{i_{1},\mspace{11mu} \ldots \mspace{14mu},i_{k}}^{1,k} \right\rbrack}^{*}.} & (10)\end{matrix}$

In the case of an OFDM system, a narrow band channel model as in Eq. 1,can be assumed for each sub-carrier. Since the channel matrices arehighly correlated among adjacent sub-carriers, the same precoder can beused in several consecutive sub-carriers. In this case, the SINRs andLMMSE filters can be determined for the channel seen on each sub-carrierusing the above expressions. Moreover in this case, the effective SINRfor the precoding matrix of rank k can be obtained using any one of thestandard combining formulae. For instance, the effective SINR can bedetermined as:

$\begin{matrix}{{\sum\limits_{i \in \Omega}{\sum\limits_{p = 1}^{k}{{\ln \left( {1 + {SINR}_{p}^{i}} \right)}/{\Omega }}}},} & (11)\end{matrix}$

where SINR_(p) ^(i) denotes the SINR computed for the stream p andsubcarrier i using Eq. 9 and where Ω denotes the set of subcarriersusing the same precoder.

Due to the nested structure of the codebook, the SINR computations andprecoder selection are considerably simplified by avoiding redundantcomputations.

4×2 Embodiment

An exemplary embodiment of a system with a transmitter having fourantennas (m=4), will now be described. In this embodiment, there are 16possible precoder matrices per rank and the following vector codebooksare used:

{v _(i) ¹ εC ⁴}_(i=1) ⁴ , {v _(j) ² εC ³}_(j=1) ⁴, [1,0]^(T) εC ².  (12)

In the case of a UE with two receive antennas (n=2), transmission canoccur in rank-1 or rank-2. The 16 possible precoder matrices for rank-2are obtained as:

$\begin{matrix}{{{A\left( {v_{i}^{1},v_{j}^{2}} \right)} = \left\lbrack {v_{i}^{1},{{{HH}\left( {v_{i}^{1} - e_{1}^{4}} \right)}\begin{bmatrix}0 \\v_{j}^{2}\end{bmatrix}}} \right\rbrack},{1 \leq i},{j \leq 4.}} & (13)\end{matrix}$

The 16 possible precoder matrices for rank-1 are obtained as the secondcolumns of all 16 possible matrices {A(v_(i) ¹,v_(j) ²)}, respectively.

An exemplary CQI-metric based selection scheme will now be described.For simplicity, the receiver can be assumed to be an LMMSE receiver andthe channel can be assumed to obey a flat fading model. In an OFDMsystem where the same precoder is used over several consecutivesub-carriers (referred to as a cluster), the following steps (with somestraightforward modifications) are performed once for each sub-carrierin the cluster. To reduce complexity, however, a few representativesub-carriers from the cluster can be selected and the following stepsperformed once for each representative sub-carrier.

For a channel estimate matrix H=[h₁,h₂,h₃,h₄] of size 2×4, the followingmatrices are determined:

HA(v _(i) ¹ ,v _(j) ²)=[Hv _(i) ¹ ,{tilde over (H)}v _(j) ²−α_(i,j)(Hv_(i) ¹ −h ₁)],  (14)

where {tilde over (H)}=[h₂,h₃,h₄] and the complex scalars{α_(i,j)}_(i,j=1) ⁴ are channel-independent factors that arepre-computed and stored at the UE. The optimal rank-1 precoding matrixcan be determined as:

arg max_(i,j) ∥{tilde over (H)}v _(j) ²−α_(i,j)(Hv _(i) ¹ −h ₁)∥².  (15)

The following matrices are then computed:

$\begin{matrix}\begin{matrix}{W^{i,j} = {\left( {{HA}\left( {v_{i}^{1},v_{j}^{2}} \right)} \right)^{*}{{HA}\left( {v_{i}^{1},v_{j}^{2}} \right)}}} \\{= \begin{bmatrix}{{Hv}_{i}^{1}}^{2} & {\left( {Hv}_{i}^{1} \right)^{*}\left( {{\overset{\sim}{H}v_{j}^{2}} - {\alpha_{i,j}\left( {{Hv}_{i}^{1} - h_{1}} \right)}} \right)} \\{\left( {{\overset{\sim}{H}v_{j}^{2}} - {\alpha_{i,j}\left( {{Hv}_{i}^{1} - h_{1}} \right)}} \right)^{*}{Hv}_{i}^{1}} & {{{\overset{\sim}{H}v_{j}^{2}} - {\alpha_{i,j}\left( {{Hv}_{i}^{1} - h_{1}} \right)}}}^{2}\end{bmatrix}}\end{matrix} & (16)\end{matrix}$

and the optimal rank-2 precoding matrix is determined as:

$\begin{matrix}{{\arg \; {\min_{i,j}{\left( {\frac{I}{\rho} + W^{i,j}} \right)_{1,1}^{- 1}\left( {\frac{I}{\rho} + W^{i,j}} \right)_{2,2}^{- 1}}}},} & (17)\end{matrix}$

where ρ=P/N₀, P is the average power per stream and N₀ is the noisevariance. Note that in the OFDM case, the optimal precoder for a clusteris determined using the corresponding effective SINRs which are obtainedusing the combining formula described above.

The MMSE filters are then determined for the optimal precoder asdescribed above.

The effective SINRs for the precoders selected for rank-1 and rank-2 aredetermined as described above. A more detailed description for a 4×2embodiment is found in the aforementioned U.S. Provisional PatentApplication No. 60/888,193, which is incorporated herein by reference inits entirety.

In a further exemplary embodiment, there are 32 possible precodermatrices per rank and the following vector codebooks are used used:

{v _(i) ¹ εC ⁴}_(i=1) ⁸ ,{v _(j) ² εC ³}_(j=1) ⁴,[1,0]^(T) εC ².  (18)

Due to the nested structure of the codebook, significant complexitysavings can be achieved by avoiding the redundant computations otherwiseinvolved. The savings in computational complexity (e.g., number ofmultiplications) achieved by the present invention over otherapproaches, including other structured codebook approaches such as thatdescribed in “Codebook Design for E-UTRA MIMO Pre-coding,” Document No.R1-062650, TSG-RAN WG1 Meeting #46bis, Seoul, South Korea, Oct. 9-13,2006, can be quantified. In the case of 16 possible precoder matrices,for rank-2, the exemplary codebook implementation of the presentinvention results in L×118 fewer multiplications, where L is the numberof representative sub-carriers used for precoder selection. For rank-1,there are L×64 fewer multiplications with the exemplary precoder schemeof the present invention. In the case of 32 possible precoder matrices,for rank-2, the exemplary codebook implementation of the presentinvention results in L×280 fewer multiplications, and for rank-1, L×168fewer multiplications. The savings over unstructured codebook schemesare even greater.

Multi-Codeword Transmission

The exemplary transmitter and receiver described above with reference toFIGS. 2 and 3, respectively, can be readily extended for multi-codewordtransmission. For q codeword transmission, where q can be at most m, thenumber of transmitting antennas, the p^(th) codeword (where 1≦p≦q) istransmitted using k_(p) streams along k_(p) columns of the precodermatrix. The precoder rank is

$k = {\sum\limits_{p = 1}^{q}{k_{p}.}}$

Furthermore, when the CQI for the p^(th) codeword is below a threshold,k_(p)=0, so that the p^(th) codeword is not transmitted.

For an m×k precoder matrix Q of rank k, a mapping rule decides the splitk→(k₁, . . . , k_(q)) as well as the column indices of Q that the k_(p)streams of the p^(th) codeword, where 1≦p≦q, should be sent along. For agiven precoder matrix, split and choice of column indices, the SINRs foreach codeword can be computed using the formulae given above (withsimple modifications). Then, for a given precoder matrix, the optimalsplit and choice of column indices is the one which maximizes theanticipated transmission rate, which itself can be determined from thecomputed SINRs. Finally, the optimal precoder matrix is the one whichalong with its optimal split and choice of column indices, yields thehighest anticipated transmission rate.

FIG. 5 shows a block diagram of an exemplary embodiment of a q codewordtransmitter 500 based on the architecture of the transmitter 200 shownin FIG. 2. As shown in FIG. 5, each of the q data streams is FEC encodedand modulated independently. Moreover, a CQI for each of the q datastreams as well as mapping data are fed-back from the receiver.

FIG. 6 shows a block diagram of an exemplary embodiment of a q codewordlinear receiver 600 based on the architecture of the receiver 300 shownin FIG. 3. The receiver 600 can operate with the transmitter 500 of FIG.5. In this embodiment, the q codewords are demodulated and then FECdecoded independently.

FIG. 7 shows a block diagram of an exemplary embodiment of a q codewordreceiver 700 incorporating successive interference cancellation (SIC).In this embodiment, each of q−1 recovered data streams, corresponding tocodewords 1 through q−1, is re-encoded by a FEC encoder 735 andre-modulated by a modulator 737, and then fed-back to the detector 710.

The mapping information fed back from the receiver includes the splitand the choice of column indices. The mapping rule can also be fixed, orvaried slowly (“semi-static”). In this case, each m×k precoder matrix Qis associated with one split (k₁, . . . , k_(q)) and one choice ofcolumn indices. With a fixed or semi-static mapping rule, the receiverneed not feed-back mapping information to the transmitter because it canbe inferred by the transmitter based on just the precoder matrix indexthat is fed-back.

It is understood that the above-described embodiments are illustrativeof only a few of the possible specific embodiments which can representapplications of the invention. Numerous and varied other arrangementscan be made by those skilled in the art without departing from thespirit and scope of the invention.

1. A method of operating a multi-rank beam forming (MRBF) systemcomprising generating a feedback index for transmission to a remotetransmitter comprising selecting a precoder index from a codebook ofprecoding matrices wherein the plurality of precoder matrices have anested structure and are derived from a set of vector codebooksdetermined in accordance with the following expression:${{A\left( {v_{i_{1}}^{1},v_{i_{2}}^{2},v_{i_{3}}^{3},\ldots}\mspace{14mu} \right)} = \begin{bmatrix}{v_{i_{1}}^{1},{{{HH}\left( {v_{i_{1}}^{1} - e_{1}^{M}} \right)}\begin{bmatrix}0 \\v_{i_{2}}^{2}\end{bmatrix}},} \\{{{HH}\left( {v_{i_{1}}^{1} - e_{1}^{M}} \right)}\mspace{11mu}} \\{\begin{bmatrix}0 \\{{{HH}\left( {v_{i_{2}}^{2} - e_{1}^{M - 1}} \right)}\begin{bmatrix}0 \\v_{i_{3}}^{3}\end{bmatrix}}\end{bmatrix},\ldots}\end{bmatrix}},$ and wherein e₁ ^(N)=[1, 0, . . . , 0]^(T)εC^(N), M isthe number of transmit antennas, C^(N) is an N-dimensional complexspace, ${{HH}(w)} = \left\{ {\begin{matrix}{I - {2\frac{{ww}^{H}}{{w}^{2}}}} & {{{if}\mspace{14mu} w} \neq 0} \\I & {{{if}\mspace{14mu} w} = 0}\end{matrix}\mspace{14mu} {and}\mspace{14mu} \left\{ {v_{i_{j}}^{j} \in C^{M - j + 1}} \right\}} \right.$is a vector codebook and v_(i) ^(α) is selected from a set V^(α) whereV¹={v_(i) ¹εC^(M)}_(i=1) ^(N) ¹ , V²={e₁ ^(M-1)}, V³={e₁ ^(M-2)}, . . ..
 2. The method of claim 1 wherein deriving a precoding matrix of rank-kcomprises generating a square matrix using the expression${A\left( {v_{i_{1}}^{1},v_{i_{2}}^{2},v_{i_{3}}^{3},\ldots}\mspace{14mu} \right)} = \begin{bmatrix}{v_{i_{1}}^{1},{{{HH}\left( {v_{i_{1}}^{1} - e_{1}^{M}} \right)}\begin{bmatrix}0 \\v_{i_{2}}^{2}\end{bmatrix}},} \\{{HH}\left( {v_{i_{1}}^{1} - e_{1}^{M}} \right)} \\{\begin{bmatrix}0 \\{{{HH}\left( {v_{i_{2}}^{2} - e_{1}^{M - 1}} \right)}\begin{bmatrix}0 \\v_{i_{3}}^{3}\end{bmatrix}}\end{bmatrix},\ldots}\end{bmatrix}$ and picking any k of its columns.
 3. The method of claim2 comprising: selecting the precoder matrix from a plurality of precodermatrices.
 4. The method of claim 3, wherein the step of selecting theprecoder matrix includes: estimating a channel over which the precodedmodulated symbols are to be transmitted; determining a channel qualitymetric for each of the plurality of precoder matrices; and selecting theprecoder matrix for which the channel quality metric is greatest.
 5. Themethod of claim 4 wherein determining a channel quality metric for eachof the plurality of precoder matrices exploits the nested structure ofsaid matrices
 6. The method of claim 4 wherein exploiting the nestedstructure of a first precoding matrix involves reusing some of thecomputations made in determining the channel quality metric of a secondprecoder matrix which is a sub-matrix of the first precoding matrix 7.The method of claim 1, wherein a scaled version of the precoder is used.8. The method of claim 1, wherein the number of transmit antennas is 4.9. The method of claim 1, wherein the number of transmit antennas is 2.10. The method of claim 2, wherein the number of selected columns toform a precoder is less than the number of transmit antennas.
 11. Themethod of claim 2, wherein all the columns are selected to form aprecoder.